The Italian motors giant has owned a majority stake in the US company since 2009.
The agreement ends drawn-out negotiations with the current owners, Veba, the healthcare trust affiliated to the United Auto Workers’ union.
Chrysler and Fiat will pay the trust an initial $3.65 billion.
Once the deal is signed off, Chrysler will pay Fiat another $700 million.
Fiat’s chief executive, Sergio Marchionne, plans to widen the company’s global reach.
The Veba trust looks after medical benefits for retired Chrysler workers.
The alliance between the two companies came amid the major restructuring of the US car industry following the financial crisis of the late 2000s.
The link-up gave Fiat access to the vast US car market, while Chrysler was able to benefit from the Italian firm’s expertise in developing small, fuel efficient vehicles.
Recently, Chrysler reported a 22% rise in third-quarter profits to $464 million, with net revenue up 13.5% to $17.6 billion.
Chrysler said its results had been helped by strong sales of its Jeep Grand Cherokee and the Ram 1500 pickup.
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